Optical fiber transmission systems are subject to distortion related to loss, noise, and nonlinearities in both the fiber and the modulation and amplification devices. One of the more deleterious forms of signal distortion is that due to chromatic dispersion. Chromatic dispersion in optical fiber is typically characterized by a linear (non-flat) group delay parameter. The group refractive index of the fiber at optical frequencies near a given optical carrier frequency varies approximately linearly with wavelength or optical frequency about the carrier. This finite linear group delay imposes a quadratic phase rotation across the signal frequency band which translates to intersymbol interference in the time domain signal. The fact that a large portion of the fiber in use today is dispersive at the desired operating wavelengths dictates that economic solutions are required.
Approaches currently used to reduce the effects of chromatic dispersion include: (1) reversing the effects of chromatic dispersion in the optical domain, (2) reversing the effects in the electrical domain after optical detection and (3) reducing the transmission bandwidth of the optical signal on the fiber. The first is based on purely optical methods where the effects of group velocity dispersion are reversed while the signal is still in the optical domain. Adding dispersion compensating fiber in the transmission path is one common approach. Other optical methods include compensation by differential time delay of the upper and lower sidebands of the modulated signal, see A. Djupsjobacka, O. Sahlen, xe2x80x9cDispersion compensation by differential time delay,xe2x80x9d IEEE Journal of Lightwave Technology, vol. 12, no. 10, pp. 1849-1853, October 1994, spectrally inverting the signal at the midpoint of the transmission path, see R. M. Jopson, A. H. Gnauck, R. M. Derosier, xe2x80x9c10 Gb/s 360-km transmission over normal-dispersion fiber using mid-system spectral inversion,xe2x80x9d Proceedings OFC""93, paper PD3, 1993; and pre-chirping the transmitted signal in an external modulator, see F. Koyama, K. Iga, xe2x80x9cFrequency chirping in external modulators,xe2x80x9d IEEE Journal of Lightwave Technology, vol. 6, no. 1, pp. 87-03, January 1988, and A. H. Gnauck, S. K. Korotky, J. J. Veselka, J. Nagel, C. T. Kemmerer, W. J. Minford, D. T. Moser, xe2x80x9cDispersion penalty reduction using an optical modulator with adjustable chirp,xe2x80x9d IEEE Photonics Technology Letters, vol. 3, no. 10, pp. 916-918, October 1991.
The second approach, in which dispersion effects are reversed in the electrical domain, is based on coherent transmission and homodyne detection followed by equalization in the electrical domain. Homodyne detection is only effective on single sideband signals. If homodyne detection were attempted with a DSB signal, the upper and lower sidebands would overlap upon detection and the phase information would be lost and the higher modulation frequencies severely attenuated or distorted through frequency selective fading. Some techniques used or proposed for post-detection equalization include the use of microstrip lines, see K. Iwashita, N. Takachio, xe2x80x9cChromatic dispersion compensation in coherent optical communications,xe2x80x9d Journal of Lightwave Technology, vol. 8, no. 3, pp. 367-375, March 1990; microwave waveguides, see J. H. Winters, xe2x80x9cEqualization in coherent lightwave systems using microwave waveguides,xe2x80x9d Journal of Lightwave Technology, vol. 7, no. 5, pp. 813-815, May 1989, and fractionally spaced equalizers, see J. H. Winters, xe2x80x9cEqualization in coherent lightwave systems using a fractionally spaced equalizer,xe2x80x9d Journal of Lightwave Technology, vol. 8, no. 10, pp. 1487-1491, October 1990.
The third approach is to modify the transmission format so that the baseband signal spectrum is compressed. These types of approaches, which reduce the transmission bandwidth required on the fiber to transmit a given bit rate, are generally implemented by modifying the line code format in order to reduce the effective bandwidth required to transmit or receive the data, see K. Yonenaga, S. Kuwano, S. Norimatsu, N. Shibata, xe2x80x9cOptical duobinary transmission system with no receiver sensitivity degradation,xe2x80x9d Electronic Letters, vol. 31, no. 4, pp. 302-304, February 1995, and G. May, A. Solheim, J. Conradi, xe2x80x9cExtended 10 Gb/s fiber transmission distance at 1538 nm using a duobinary receiver,xe2x80x9d IEEE Photonics Technology Letters, vol. 6, no. 5, pp. 648-650, May 1994.
More recently it has been shown that optical single sideband transmission (OSSB) can combat some of the deleterious effects of chromatic dispersion. OSSB provides a dispersion benefit directly by reducing the signal bandwidth and also by aiding in the signal restoration through post-detection dispersion compensation. The generation, transmission and detection of single sideband (SSB) signals has been used for both baseband and the RF and microwave regions of the electromagnetic spectrum to reduce the bandwidth of the signal by a factor of two, by sending either the upper or the lower sideband. Generation and transmission of OSSB optical signals using a Mach-Zehnder modulator is shown in M. Izutsu, S. Shikama, T. Sueta, xe2x80x9cIntegrated optical SSB modulator/frequency shifter,xe2x80x9d IEEE Journal of Quantum Electronics, vol. QE-17, no. 11, pp. 2225-2227, November 1981, and R. Olshansky, xe2x80x9cSingle sideband optical modulator for lightwave systems,xe2x80x9d U.S. Pat. No. 5,301,058, 1994. Methods based on AM compatible radio modulators were outlined in Jan Conradi, Bob Davies, Mike Sieben, David Dodds and Sheldon Walklin, xe2x80x9cOptical Single Sideband (OSSB) Transmission for Dispersion Avoidance and Electrical Dispersion Compensation in Microwave Subcarrier and Baseband Digital Systemsxe2x80x9d, OFC 97 Postdeadline, February 1997, and M. Sieben, J. Conradi, D. Dodds, B. Davies, and S. Walklin xe2x80x9c10 Gbit/s optical single sideband systemxe2x80x9d Electronics Letters Vol. 33, No. 11, pp 971-973. Sieben; Michael J., Conradi; Jan, Dodds; David E., U.S. Pat. No. 5,880,870, Mar. 9, 1999 Optical modulation system Robert J. Davies, Jan Conradi, David Dodds, Hybrid Single Sideband Optical Modulator. U.S. Pat. No. 5,999,300, Dec. 7, 1999., and Robert J. Davies, Minimum Phase Dispersion Compensator, U.S. Pat. No. 5,949,926, Sep. 7, 1999. The structures outlined in these documents addressed the need for large added carrier in the transmitted optical signal by using approximations to time domain minimum phase signals with single sideband properties. This allowed the transmitted information to be directly modulated onto the optical electric field envelope while a special phase function was incorporated into the AM signal to cancel all or part of an information sideband.
While in digital optical SSB modulation a dispersion benefit accrues directly due to the fact that the transmitted signal spectrum has been reduced, the more significant advantage of optical SSB transmission is that the fiber dispersion can be compensated in the electrical domain after detection. This advantage is similar to that for heterodyne detection of DSB signals, but with SSB transmission and detection, the signal can be homodyned directly to baseband using carrier signal added either at the source or at the receiver and thus it can be directly detected with the phase or delay information of the transmitted signal preserved. This was shown in K. Yonenaga, N. Takachio, xe2x80x9cA Fiber chromatic dispersion compensation technique with an optical SSB transmission in optical homodyne detection systems,xe2x80x9d IEEE Photonics Technology Letters, vol. 5, no. 8, pp. 949-951, August 1993, where integrated optical structures were used to generate single sideband tones for narrowband applications. In K. Yonenaga, N. Takachio, xe2x80x9cDispersion compensation for homodyne detection systems using a 10 Gb/s optical PSK-VSB signal,xe2x80x9d IEEE Photonics Technology Letters, vol. 7, no. 8, pp. 929-931, August 1995, a single sideband optical modulator was described for the purpose of transmitting two or more optical signals with different optical carrier frequencies on a single fiber. The purpose of transmitting the signals in a single sideband format is to permit these optical carrier frequencies to be spaced as closely as the maximum modulation frequency. A fundamental disadvantage of this type of dispersion compensation is found in the fact that the carrier power added to the transmitted signal must be significant thus reducing the potential signal to noise ratio at the transmitter.
To improve this situation the virtues of polybinary (or duo-binary) modulation may be applied. The term polybinary refers to a modification of a binary signal in which the levels have been altered so as to maintain the information while removing some of the DC content of the signal and reducing the bandwidth. The most common implementation of this type of signal is the duobinary signal where a two level binary signal is converted to a three level signal represented by a zero voltage level and two levels symetrically located at positive and negative voltage levels with respect to the zero voltage level. The non-zero voltage level represent logical zeros and the zero level represents logical ones. These signals are part of a class of signals referred to as correlative coding or partial response signals, so named because they allow a controlled amount of inter-symbol interference to achieve another advantage such as reduced bandwidth and reduced dc content. See Lender, A., xe2x80x9cThe Duo-Binary Technique of High Speed Data Transmission.xe2x80x9d AIEE Transaction on Communication Electronics,xe2x80x9d vol. 82, pp 214-218.
The coding rule for a duobinary signal generated from a binary signal where a logical zero or a xe2x80x98spacexe2x80x99 is represented by xe2x88x921 and a logical one or a xe2x80x98markxe2x80x99 is represented by a +1 is given by
ck=bk+bkxe2x88x921xe2x80x83xe2x80x83(1) 
where bk is the kth element of binary sequence defined above. The resulting 3 level sequence is called a duo-binary sequence and the data sequence bk may be recovered from ck by the following rule
bk=ckxe2x88x92bkxe2x88x921xe2x80x83xe2x80x83(2) 
The immediate advantage of this type of signal is a reduced bandwidth requirement for a given information rate. The disadvantage is related to the fact that a single symbol error will propagate through the data sequence due to correlation between the symbols. To overcome this a precoding scheme may be used. In this case the binary information is unipolar in that a mark is represented as a 1 and a space is represented as a 0. An intermediate pre-coded sequence is generated as in
xe2x80x83ak=bk⊕akxe2x88x921xe2x80x83xe2x80x83(3)
where ⊕ denotes modulo-2 addition. The precoder output is scaled so that a space is represented as a xe2x88x921 and a mark is represented as a +1. The precoded sequence is used to produce the duobinary sequence according to (1) above (ck=ak+akxe2x88x921) with the added advantage that the duobinary sequence so generated has independent symbols and is immune to error propagation. The data may be recovered in envelope detection format by simply determining the magnitude of the duobinary signal and scaling so that the recovered data sequence is represented by 1xe2x80x2s and 0xe2x80x2s as in                                           b            ^                    k                =                  {                                                                      0                                                                                                  1                    ,                                                                        ⁢                                                                                                      "LeftBracketingBar"                                              c                        k                                            "RightBracketingBar"                                         greater than                     1                                                                                                                                          "LeftBracketingBar"                                              c                        k                                            "RightBracketingBar"                                        ≤                    1                                                                                                          (        4        )            
A sample data sequence with precoding and duobinary encoding is shown in Table 1.
The information sequence bk is mapped into ck such that the individual symbols are independent and the bandwidth requirement for a given information rate is halved. Other types of correlative coding are possible if the coding rule is allowed to be more complicated. Some of these more complicated schemes are known as modified duobinary and alternate mark inversion. Additionally a binary signal may be mapped into a multilevel or polybinary signal where there are 5, 7 or more amplitude levels.
The spectral density function of the duo-binary signal based on the coding rule above is given by                               H          ⁡                      (            f            )                          =                  {                                                                      2                  ⁢                                      cos                    ⁡                                          (                                              π                        ⁢                                                  xe2x80x83                                                ⁢                        f                        ⁢                                                  xe2x80x83                                                ⁢                                                  T                          b                                                                    )                                                        ⁢                                      exp                    ⁡                                          (                                                                        -                          j                                                ⁢                                                  xe2x80x83                                                ⁢                        π                        ⁢                                                  xe2x80x83                                                ⁢                        f                        ⁢                                                  xe2x80x83                                                ⁢                                                  T                          b                                                                    )                                                                                                                                        "LeftBracketingBar"                    f                    "RightBracketingBar"                                    ≤                                      1                                          2                      ⁢                                              T                        b                                                                                                                                                0                                            otherwise                                                                        (        5        )            
From the optical direct detection perspective, the reduction of the dc component compared to the binary case and the bandwidth reduction inherent in duobinary coding are the most favourable benefits of duobinary signaling along with the fact that the signal is recoverable by envelope detection. Complete removal of the dc component may be achieved for a different coding rule known as modified duo-binary. In this case the precoder rule is given by
ak=bk⊕akxe2x88x922xe2x80x83xe2x80x83(6) 
and the correlation span for the coder is 2 digits rather than 1 as in
ck=akxe2x88x92akxe2x88x922xe2x80x83xe2x80x83(7) 
Table 2 shows the modified duobinary coding method.
The spectral density for the modified duo-binary coding rule is given by                               H          ⁡                      (            f            )                          =                  {                                                                      2                  ⁢                  j                  ⁢                                      xe2x80x83                                    ⁢                                      sin                    ⁡                                          (                                              π                        ⁢                                                  xe2x80x83                                                ⁢                        f                        ⁢                                                  xe2x80x83                                                ⁢                                                  T                          b                                                                    )                                                        ⁢                                      exp                    ⁡                                          (                                                                        -                          j                                                ⁢                                                  xe2x80x83                                                ⁢                        π                        ⁢                                                  xe2x80x83                                                ⁢                        f                        ⁢                                                  xe2x80x83                                                ⁢                                                  T                          b                                                                    )                                                                                                                                        "LeftBracketingBar"                    f                    "RightBracketingBar"                                    ≤                                      1                                          2                      ⁢                                              T                        b                                                                                                                                                0                                            otherwise                                                                        (        8        )            
where it is noted that the DC component is zero valued. Thus for a trade-off in coder length, an SNR advantage is gained in the sense that none of the finite power of the optical signal is wasted on the non-information carrying DC or carrier component of the signal.
For the polybinary case we may consider the case where a binary signal is converted into a signal with j levels that are numbered form 0 to jxe2x88x921. The coding rule in this case is given by
ak=bk⊕akxe2x88x921⊕akxe2x88x922⊕ . . . akxe2x88x92(jxe2x88x922)xe2x80x83xe2x80x83(9) 
The precoded sequence is then converted to the j level signal using
ck=ak+akxe2x88x921+ . . . +akxe2x88x92(jxe2x88x922)xe2x80x83xe2x80x83(10) 
where the spaces in the sequence xe2x80x98axe2x80x99 have been changed from zero to xe2x88x921. Note that the correlation span now covers a length of jxe2x88x921 digits. The demodulation rule is slightly more difficult than the duo-binary case in that marks are taken from the odd levels in the polybinary sequence and the spaces are taken from the even levels. Nonetheless the information is still recoverable using envelope detection techniques.
This invention provides an improvement over both polybinary signaling and optical single sideband by implementing polybinary modulation on a single sideband modulator. This action combines the chromatic dispersion advantages of SSB modulation with the DC level and bandwidth reduction of duo-binary coding.
Therefore there is provided an apparatus for modulating information bearing symbols onto an optical carrier, the apparatus comprising a polybinary coder that operates on a binary information signal to produce an envelope compatible polybinary signal; and an optical single sideband modulator that modulates an optical carrier with the envelope compatible polybinary signal to produce a single sideband optical signal.
In a further aspect of the invention, the polybinary coder produces an envelope compatible polybinary signal by dividing a polybinary signal into at least a pair of unipolar signals. In a further aspect of the invention, the polybinary coder produces an envelope compatible polybinary signal by separately operating on a polybinary signal in a first stream to convert all negative symbols in the polybinary stream to zero symbols and in a second stream to convert all positive symbols in the polybinary signal to zero symbols.
In a further aspect of the invention, the optical single sideband modulator operates on the optical carrier using the envelope compatible polybinary signal to produce a single sideband optical signal whose phase is determined by operating on the output of the polybinary coder with a Hilbert transform and whose magnitude is determined by the magnitude of the output of the polybinary coder. The output of the polybinary coder may be converted by a logarithmic operator prior to input to the Hilbert transform. The output of the polybinary coder may be adjusted to avoid singularities in the operation of the logarithmic operator.